Bizarre grey object within mesh area?
Unselectable geometry in Edit mode means there's another object in the scene located in the same place. You have several options to continue working on current object without anything messing around:


enter Local View for selected object. Nothing except it will be visible. Note that you can activate Local View for several selected objects, not only one;
exit Edit mode and enter Object mode. From there you'll be able to select another object (you could use Outliner for navigating the objects in the scene in order to find what's needed) and either move it somewhere else or delete it altogether.  
join objects, which is done from Object mode too. Thus both objects will be editable at the same time, see Cannot select vertices from different object while in edit mode. Note that you could edit 2 different objects without joining them with MultiEdit addon;